Quantitative Determination of Quantum Fluctuations in Clean Magnets I: Neutron Spin Echo

Starting from the magnetic total-moment sum rule of neutron scattering, we derive an explicit connection between ordered-moment reduction and the long-time limit of the intermediate scattering function. We show that this time-domain formulation establishes a direct and experimentally accessible measure of quantum fluctuation strength through neutron spin-echo spectroscopy, with \[P(t\rightarrow\infty)=\frac{I(Q,t\rightarrow\infty)}{I(Q,t=0)}=\frac{\langle μ\rangle^{2}}{\langle μ^{2} \rangle}\] This identity links the long-time polarization to the ratio between ordered and total magnetic moments. Linear spin-wave calculations for square and triangular Heisenberg antiferromagnets demonstrate that both quantum spin reduction and geometric frustration suppress the plateau value in quantitative agreement with moment reduction. The resulting framework establishes a direct and model-independent measure of the level of quantum fluctuations in bulk quantum magnets, particularly for polycrystalline samples.